A triangle inscribed onside a semi circle with diameter as the hypotenuse and a vertex on curved boundary of semicircle is always a right triangle. An isosceles right triangle is a right triangle, in which adjacent sides(non hypotenuse sides) of right angle are equal in length.

Axioms. An axiom is an established or accepted principle. For this section, the following are accepted as axioms. The theorem of Pythagoras states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. The converse of "A implies B" is "B implies A". The isosceles triangle theorem states that if two sides of a triangle are the same, then two angles of that triangle are the same.